If you are learning the API, it is a very good idea to use the test network (run bitcoind -testnet and bitcoin-cli -testnet).

JSON-RPC

Running Bitcoin with the -server argument (or running bitcoind) tells it to function as a HTTP JSON-RPC server, but
Basic access authentication must be used when communicating with it, and, for security, by default, the server only accepts connections from other processes on the same machine. If your HTTP or JSON library requires you to specify which 'realm' is authenticated, use 'jsonrpc'.

Bitcoin supports SSL (https) JSON-RPC connections beginning with version 0.3.14. See the rpcssl wiki page for setup instructions and a list of all bitcoin.conf configuration options.

Allowing arbitrary machines to access the JSON-RPC port (using the rpcallowip configuration option) is dangerous and strongly discouraged-- access should be strictly limited to trusted machines.

Proper money handling

Languages

Python

python-jsonrpc is the official JSON-RPC implementation for Python.
It automatically generates Python methods for RPC calls.
However, due to its design for supporting old versions of Python, it is also rather inefficient.
jgarzik has forked it as Python-BitcoinRPC and optimized it for current versions.
Generally, this version is recommended.

While BitcoinRPC lacks a few obscure features from jsonrpc, software using only the ServiceProxy class can be written the same to work with either version the user might choose to install:

Note: The jsonRPCClient library uses fopen() and will throw an exception saying "Unable to connect" if it receives a 404 or 500 error from bitcoind. This prevents you from being able to see error messages generated by bitcoind (as they are sent with status 404 or 500). The EasyBitcoin-PHP library is similar in function to JSON-RPC PHP but does not have this issue.

Java

The easiest way to tell Java to use HTTP Basic authentication is to set a default Authenticator:

Qt/C++

QJsonRpc is a Qt/C++ implementation of the JSON-RPC protocol. It integrates nicely with Qt, leveraging Qt's meta object system in order to provide services over the JSON-RPC protocol. QJsonRpc is licensed under the LGPLv2.1.

Multi-wallet RPC calls

Bitcoin Knots 0.13.1 added support for loading multiple, separate wallets.
Multi-wallet can be enabled by using more than one -wallet argument when starting Bitcoin, either on the command line or in the Bitcoin config file.
This was also included in Bitcoin Core 0.15.

Wallet-level RPC calls (like importaddress or listtransactions) can specify which wallet file will be accessed. This is done by setting the HTTP endpoint in the JSON-RPC request in the format <RPC IP address>:<RPC port>/wallet/<wallet name>, for example https://127.0.0.1:8332/wallet/wallet1.dat.

The command line utility bitcoin-cli can specify the wallet file using the -rpcwallet flag, for example bitcoin-cli -rpcwallet=wallet1.dat getbalance